期刊
IET CONTROL THEORY AND APPLICATIONS
卷 12, 期 2, 页码 183-193出版社
WILEY
DOI: 10.1049/iet-cta.2017.0785
关键词
fuzzy control; adaptive control; nonlinear control systems; stability; inference mechanisms; numerical analysis; adaptive type-2 fuzzy system; chaotic nonlinear fractional order systems; synchronisation; stabilisation; adaptive interval type-2 Takagi-Sugeno-Kang fuzzy system; IT2 TSK fuzzy system; consequent parameters; inference mechanism; global Mittag-Leffler stability; closed-loop system; projection algorithm; fractional order adaptation law; supervisory mode
This study proposes an adaptive interval type-2 Takagi-Sugeno-Kang (IT2 TSK) fuzzy system with a supervisory mode to control and stabilise a certain class of non-linear fractional order systems. In this study, a fractional order adaptation law is derived which adjusts the free parameters and bounds them by utilising a projection algorithm. The global Mittag-Leffler stability of the closed-loop system is proved in the sense that all the involved signals are uniformly bounded. Moreover, if the non-linear system tends to be unstable, a supervisory controller starts cooperating with the adaptive IT2 TSK fuzzy controller to guarantee the stability of the closed-loop system. In addition, a new inference mechanism for the adaptive IT2 TSK fuzzy system is introduced for which the antecedent part is chosen as a type-2 fuzzy set and the consequent parameters are represented as interval sets. According to the practical nature of the proposed inference equation, it would be applicable in online and real-time applications. Numerical simulations show the validity and effectiveness of the introduced control strategy for stabilisation and control of a general class of non-linear fractional order systems perturbed by disturbance and uncertainty.
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